21st Century Fox abruptly abandoned its takeover pursuit of Time Warner Inc., citing both Time Warner's unwillingness to "engage with us" and a sharp drop in Fox's stock price which made a deal "unattractive to Fox shareholders."

Fox's stock had fallen about 11% since news broke last month that it had made a takeover offer for Time Warner valued at $85 a share, or about $80 billion, in a mix of cash and stock. Time Warner rejected the offer, but Fox had signaled it was prepared to continue fighting,...